[Zurück]

C. Carstensen, D. Praetorius:
"Averaging Techniques for the A Posteriori BEM Error Control for a Hypersingular Integral Equation in Two Dimensions";
SIAM Journal on Scientific Computing, 29 (2007), 2; S. 782 - 810.

Averaging techniques or gradient recovery techniques are frequently employed
tools for the a~posteriori finite element error analysis. Their very recent
mathematical justification for partial differential equations allows
unstructured meshes and non-smooth exact solutions. This paper establishes an
averaging technique for the hypersingular integral equation on a
one-dimensional boundary and presents numerical examples for supporting that
averaging techniques can be employed for an effective mesh-refining
algorithm. For the discussed test examples, the provided estimator estimate
the (in general unknown) error very accurately in the sense that the quotient
{\em error/estimator} stays bounded with a value close to $1$.

http://dx.doi.org/10.1137/050623930

http://www.anum.tuwien.ac.at/~dirk/download/published/ccdpr05_sisc29.pdf